The whole reason "empty chamber" even crosses a person's mind is because of the paranoia and fear of a negligent/accidental discharge.
It is reasonable to have concern over this issue. That is fine. However, turing a gun into a throwing rock by not chambering a round defeats the purpose of having a gun. No instructor on Earth (that is competent) would advocate that you draw, chamber, then fire. It is just absurd.
Trust the safety mechanisms of the gun - they will work. Such devices are hammer blocks, firing pin blocks, striker blocks etc. This prevents the gun from going off if a spring or pin breaks. In other words, mechanical failure still can't make the gun go off. Nothing will make it discharge except for spontaneous ignition of the primer or powder which is probably 1:1,000,000,000,000 odds.
So the only thing you have to worry about is that trigger.
DO THIS:
Take the gun you want to carry concealed. Take out the magazine. UNLOAD the gun. Check the chamber. Be sure it isn't loaded. Now, rack the slide, and make sure the gun is cocked. If a 1911, put safety on. If a Glock, rack to make sure tension is on the striker. This allows you to determine if the gun would have discharged or not in the following test.
Carry it around. Test it in your home. Bend, twist, fumble around it. If in pocket, move around and about, rub against it, tug, tuck, pull, snag, stretch, poke...do whatever you can within reason to get that trigger to fully pull and hear a "click". If you can do that, I'd be impressed. It is tough to get a double action concealed carry gun's trigger to be pulled all the way back. If a 1911, see if you can get the safety disengaged at all. Don't forget, these also have grip safeties making them one of the safest guns.
**make sure the gun is UNLOADED**
Use reason. Guns without long, heavy trigger pulls should be used in a holster - that means 1911's and Glocks. If you use a holster - there is 10 times less worry about an accidental discharge. An HK USP has such a brutal double action pull, you can get away with pocket carry in a jacket or something. Same goes for double action-J frame revolvers. Kel-Tecs have long, heavy pulls. Kahr has a long heavy pull. Not only are they all long, and heavy, but they all "fire" when the trigger is completely rearward. Which is tough to do unless your using a finger.
If you pocket carry, then use a pocket holster to keep the gun upright for quick draw, and NEVER put anything like keys in the pocket that can tangle with the trigger etc..
If you have a holster, the only thing to worry about isn't discharging while in the holster, or while drawing, but while holstering (Glocks).
Common sense stuff.